Aircraft: CRJ200
Phase of flight: Final Approach
Anomaly: Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Weather / Turbulence

We had an early afternoon report and had endured mechanical and weather delays for approximately 8 hours prior to leaving; which included boarding the passengers twice prior to cancelling the flight all together. Conditions in FAY indicated that the ceilings were going to be 3;200 FT or higher and generally VFR. Ramp conditions made taxiing to the runway very arduous. Once airborne our flight was routine. During the descent we found that the conditions on the ATIS were indicating VFR with BKN 3;200 and we could see the ground at our location approximately 30 NM from the airport. ATIS further indicated LOC BC 22. We briefed the First Officer's approach plate; due to the fact that I had replaced the LOC BC 22 11-2 with the 11-1 for FAY and did not have the plate on board. We set everything up and the First Officer held the plate in his chart holder. During my brief I explained the plate for a VFR approach due to the current conditions should allow a visual landing after we go through the BKN layer. After intercepting the final approach course we descended to 2;100 FT. At ALTSCAP; the 'ALTSCAP' call was made and First Officer dialed in 1;800 FT. I descended to 1;800 FT. At ALTSCAP; the 'ALTSCAP' call was made and First Officer put in 600 FT. I then made the mistake of not looking to make sure we were past MORGY (the descent point to go from 1;800 to 600). I dial a 1;000 FT per minute descent and around 1;000 FT the ATC Controller explained he was getting a low altitude alert. We realized that we were to low and began the climb back to 1;800 FT; reaching 1;800 FT at MORGY. Being stabilized we began the descent down to our MDA of 600 FT. Once there we did not see any of the runway environment so we executed a missed approach. While receiving vectors for the ILS 04 we were told that a new ATIS was just released; Visibility - 7; ceiling - 300 FT. We executed the ILS 04 with no issue and had eyes on the runway at 200 FT AGL. The stress and issues occurring earlier in the day were a contributing factor of becoming complacent on arrival into FAY. It had been a long day and a long 2 days prior to that due to weather around the system. Having only 1 approach plate was a huge pilot error on my part. The incorrect ATIS corresponded to the TAF that we had prior to departing; so we didn't question the weather like we should have. It seemed that the weather was beginning to get worse; so if ATC could have said that we might not be able to get in on [Runway] 22 I would have immediately chosen [Runway] 04 with a slight 4-5 knot tailwind that would get me down to a lower minimum. Rest and more attention to detail could have prevented these issues. We were assigned the LOC BC 22 approach in to FAY. We were vectored into the approach at 2;100 FT and once established; descended to 1;800 FT enroute to MORGY (FAF). After Captain made the callout of 'ALTSCAP'; I entered the MDA of 600 FT into the altitude selector. On the FMS map; there was a crossing restriction of 900 FT at JONSI which Captain asked me about. I checked the approach plate and told him there was not a restriction on the plate and JONSI was only identified as the MAP on the approach plate. While I was further reviewing the plate to make sure I had given him completely accurate information; he began to descend. After I confirmed that I had given him accurate information; I began to scan outside for the airport after sensing the descent to minimums. At approximately 1;000 FT; Fayetteville Tower queried us; asking us to confirm that we were descending via the LOC BC 22 approach. It was at this point; we became aware that our descent to minimums had begun too early. We immediately returned to 1;800 FT; the published altitude prior to MORGY. Upon reaching MORGY we resumed the approach normally and executed a missed approach at the MAP (JONSI) due to not being able to see the runway. After the missed approach; the Departure/Approach Controller informed us that Tower had just updated the weather to show the ceiling at 300 AGL and lowering; I do not remember the updated visibility that was given to us. The ceiling was originally reported at 2;300 AGL and 8 SM visibility; when we had began the LOC BC 22 approach. We requested ILS 4 based on the new information; flew the approach; and landed.The early descent error could have been avoided by a final cross check of all position/navigational information before I started scanning outside for the runway rather than assuming the descent was occurring at the correct phase of the approach. My heads down time looking at the plate to make sure I had not missed any notes on the approach plate and attempting to figure out why the FMS was showing a crossing restriction at JONSI of 900 FT distracted me from doing such. The missed approach was impossible to avoid. The Tower did not update the weather report to reflect the current conditions until after we executed the missed approach; given the weather information we had; the LOC BC 22 was a valid approach assignment. CRJ-200 flight crew reports descending toward minimums prior to MORGY on the LOC BC to Runway 22 at FAY and ATCT issues a low altitude alert. The aircraft is climbed back to 1;800 FT then down to 600 FT passing MORGY; but a missed approach ensues due to the runway not being sighted. The ensuing ILS to Runway 4 is successful.